#maximum distance we are looking for
$delta = 0.01;
#test array
@a = (1.02, 1.03, 6.01, 9, 1.04, 1.011, 1.025, 1.01, 0.005, -0.002);

#"discretize" points to neighboring points, scale by 1/$delta 
#to simplify computation
for (@a) {
  push @{$h{int($_/$delta)}}, $_;
  push @{$h{int($_/$delta-1)}}, $_;
  push @{$h{int($_/$delta+1)}}, $_;
}

#handle clusters
for (keys %h) {
  #in case the corresponding array has more than one element, 
  #we know that it contains at least one pair not 
  #further apart than 2 * $delta, otherwise ignore it 
  if (@{$h{$_}} > 1) {
    @sorted = sort @{$h{$_}};
    for (0..@sorted-2) {
      $r = $sorted[$_];
      $s = $sorted[$_+1];
      #filter out neighboring pairs, since we do not need to 
      #process the numbers further, we cram them into a
      #string for the final output
      $near{"$r, $s"} = 1 if ($r < $s && $s <= $r + $delta);
    }
  }
}

print "Not further than $delta apart are the following pairs:\n";
print "$_\n" for (keys %near);

##</code><code>##

Not further than 0.01 apart are the following pairs:
-0.002, 0.005
1.02, 1.025
1.025, 1.03
1.011, 1.02
1.03, 1.04
1.01, 1.011

##</code><code>##

use strict;
use warnings;
use Benchmark;
#maximum distance we are looking for
my $delta = 0.01;
#test array
my @a;
for (1..300000) {
  push @a, rand() * 300;
}

my ($r, $s);

timethis ( 10 => 
  sub { ...